How to use multiple HDRIs
A simple solution with no compositing, is to have two images as the background material for your environment texture.
You mix them using a color mix node controlled by Is glossy Ray in the light path node. The glossy surfaces reflect one image, while others use the other HDRI image normally:

Alternatively, you can use Is Camera Ray to can have the one image not interact the objects at all but stay as backdrop for the scene:


Update for 2.8

In the shader editor, set to edit the world.